Matsu or Kinmen: NT$1800 (one way)
Buy one-way as no tax applies if you purchase the return ticket over there. Use credit cards to obtain an insurance - you never know …
Be aware that the flights are often fully booked, if you make a reservation you must pick up the ticket 20 minutes before check-in time, else it goes to somebody else. Produce your IC/ARC/Passport to identify yourself.
Also expect that flights are delayed or cancelled due to the weather conditions, currently it’s very cold and extremely windy in Matsu.
I posted some more information about Matsu and Kinmen in another thread, just run a search.
PS: I am off to work in Matsu on Monday until CNY …
Edit: currently the airport of Matsu is on PeiKan island, starting on the 24th of this month (unconfirmed) it will be in NanKan. From there you can take a boat to HsiJue - though I wouldn’t know what to do there.
For the more adventurous: there is a daily ferry (pending weather conditions) from Keelung to NanKan via DongYin and vice versa. It’s an overnight trip (7 + 2.5 hours I think) and you can take a car or small truck along.